18.2 Poker over the Telephone

Alice and Bob quickly tire of flipping coins over the telephone and decide to try poker. Bob pulls out his deck of cards, shuffles, and deals two hands, one for Alice and one for himself. Now what does he do? Alice won’t let him read the cards to her. Also, she suggests that he might not be playing with a full deck. Arguments ensue. But then someone suggests that they each choose their own cards. The betting is fast and furious. After several hundred coins (they remain unused from the coin-flipping protocol) have been wagered, Alice and Bob discover that they each have a royal flush. Each claims the other must have cheated. Fortunately, their favorite cryptologist can help.

Here is the method she suggests, in nonmathematical ...

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